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While a simple measure, it is notable in that some texts and guides suggest or imply that the dispersion of nominal measurements cannot be ascertained. It is defined for instance by ( Freeman 1965 ). Just as with the range or standard deviation , the larger the variation ratio, the more differentiated or dispersed the data are; and the smaller ...
For example, five-, seven- and nine-point scales with a uniform distribution of responses give PCIs of 0.60, 0.57 and 0.50 respectively. The first of these problems is relatively minor as most ordinal scales with an even number of response can be extended (or reduced) by a single value to give an odd number of possible responses.
Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. [1] Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal , ordinal , interval , and ratio .
A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured.
These extensions converge with the family of intra-class correlations (ICCs), so there is a conceptually related way of estimating reliability for each level of measurement from nominal (kappa) to ordinal (ordinal kappa or ICC—stretching assumptions) to interval (ICC, or ordinal kappa—treating the interval scale as ordinal), and ratio (ICCs).
A bivariate correlation is a measure of whether and how two variables covary linearly, that is, whether the variance of one changes in a linear fashion as the variance of the other changes. Covariance can be difficult to interpret across studies because it depends on the scale or level of measurement used.
For interval level variables, the arithmetic mean (average) and standard deviation are added to the toolbox and, for ratio level variables, we add the geometric mean and harmonic mean as measures of central tendency and the coefficient of variation as a measure of dispersion.
In the examples below, we will take the values given as randomly chosen from a larger population of values.. The data set [100, 100, 100] has constant values. Its standard deviation is 0 and average is 100, giving the coefficient of variation as 0 / 100 = 0